Single Sample t Test A random sample of the grade point aver

Single Sample t Test

A random sample of the grade point average of a class of 10 nursing program students from Cumberland University is provided below. The mean GPA of all nursing students at Cumberland University Is 3.23. Is the GPA of the class of 10 students greater than the GPA of the population of all Cumberland University nursing students?

Use a significance level of .05. Follow the steps in Example 9.6 of your course text.

Student GPAs:

3.0

3.5

2.3

4.0

2.7

2.9

3.2

3.7

2.6

State the null and the research hypotheses:

What is the mean of the sample?

Calculate Sum (X-M) squared.

Calculate the standard deviation of the sample(s).

What is the standard error (sx)?

List the critical value(s) needed to test the hypothesis.

Calculate the test statistic.

Based on the critical values and test statistic, what is your decision to Fail to reject the null hypothesis or reject?

Solution

Set Up Hypothesis
Null, H0: U=3.23
Alternate, H1: U<3.23
Test Statistic
Population Mean(U)=3.23
Sample X(Mean)=3.1
Standard Deviation(S.D)=0.55227
Number (n)=9
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =3.1-3.23/(0.55227/Sqrt(8))
to =-0.7062
| to | =0.7062
Critical Value
The Value of |t | with n-1 = 8 d.f is 1.86
We got |to| =0.7062 & | t | =1.86
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Left Tail -Ha : ( P < -0.7062 ) = 0.25006
Hence Value of P0.05 < 0.25006,Here We Do not Reject Ho

Fail to reject the null hypothesis